The present invention generally relates to materials and their thermal conductivities. More particularly, this invention relates to material systems capable of exhibiting changes in their thermal conductivities in response to an external control or input, and wherein such external controls/inputs may be in addition to or independent of temperature.
Thermal conductivity is an important property in heat transfer. In particular, thermal conductivity is a measure of how heat transfers through a material, and is generally intrinsically dependent on the particular material. Referring to FIG. 1, heat flux through a slab of material is determined based on equation (1):q=−kA(T1−T2)/s  Eq. (1)where q is the heat flux (the rate of heat transfer) between and transverse to two parallel surfaces of the material that are separated by a distance s, A is the cross-sectional area through which heat is transferred through the slab, k is the thermal conductivity of the material, and T1−T2 is the temperature difference between the two surfaces of the slab, where T1 represents the hotter surface and T2 represents the colder surface of the slab (i.e., T1>T2).
Equation (2) addresses the situation represented in FIG. 2 in which a slab is composed of multiple layers (in this case, three layers) that are attached to each other.q=−(T1−T2)/[s1/(k1·A1)+s2/(k2·A2)+s3/(k3·A3)]  Eq. (2)where q is the heat flux between and transverse to two parallel surfaces of the multilayer slab at temperatures T1 and T2, k1, k2, and k3 are the thermal conductivities of the respective three individual layers of the slab, A1, A2, and A3 are the cross-sectional areas of the respective three individual layers through which heat is transferred, and s1, s2, and s3 are the thicknesses of the respective three individual layers. In systems where imperfect thermal contact between individual layers of a multilayer slab is to be considered, the heat flux through the slab takes into consideration the thermal resistance attributable to contact at the interfaces between layers, and the heat flux across each interface is determined based on Equation (3):qc=−(Tc1−Tc2)/[1/(hc·Ac)]  Eq. (3)where qc is the heat flux across an interface, hc is the thermal contact conductance across the interface, Ac is the contact area of the interface, and Tc1−Tc2 is the temperature difference across the interface. The thermal contact conductance is dependent on various factors, including surface quality of the contacting surfaces and any applied contact pressure.
Thermal stresses arise when if thermal expansion of materials or structures is restricted. The thermal stress of a unidirectionally confined slab of material is based on Equation (4),σ=−Eα(T−T0)  Eq. (4)where σ is the thermal stress, E the elastic modulus of the materials, α is the coefficient of thermal expansion, and T−T0 is the difference between the stress free temperature T0 and the current temperature T.
Current theories describe thermal conductivity in solids as the migration of free electrons and lattice vibrations. These two processes are additive, but the transport due to electrons is more efficient than the transport through vibrational energy in the lattice structure of the solid. With an increase in temperature, electron motion is increasingly difficult due to the vibration of the lattice and thus the thermal conductivity is found to decline with increasing temperature, particularly for solids that are good thermal conductors such as copper, silver, and aluminum. Thus, with increasing temperatures, thermal conductivity decreases and causes the heat flux through a slab to decrease for the same temperature gradient (i.e., when one side is connected to a heat sink). For the same heat flux, the temperature gradient will be higher across the slab.
In view of the above, it can be appreciated that there are situations in which it would be desirable if the negative impact of increasing temperature on thermal conductivity could be diminished, and/or thermal conductivity could be tunable to obtain a desired response within a material system or structure, for example, the thermal conductivity of a material system or structure could be intentionally varied in a manner other than that which would be ordinarily attributable solely to temperature.